President Obama entered the debate about the national debt on Wednesday after months on the sidelines, offering a plan to trim borrowing by $4 trillion over the next 12 years by combining deep cuts in military and domestic spending with higher taxes on the wealthy.

In a stinging rebuke to Republican budget-cutters, Obama acknowledged that the debt must be tackled faster than he has previously proposed, but he rejected GOP calls to make fundamental changes to Medicare and Medicaid and to scale back his initiative to expand health-care coverage to the uninsured.

“We don’t have to choose between a future of spiraling debt and one where we forfeit investments in our people and our country,” he said. “To meet our fiscal challenge, we will need to make reforms. We will all need to make sacrifices. But we do not have to sacrifice the America we believe in. And as long as I’m president, we won’t.”

And even as he joined the battle, Obama immediately volleyed the substantive work of debt reduction back to Capitol Hill, calling on lawmakers to reach “a final agreement on a plan to reduce the deficit” before the Treasury breaches the $14.3 trillion legal limit on borrowing in early July. The country could face devastating economic consequences if it were to stop borrowing and default on its obligations.

Obama said the talks, to be led by Vice President Biden, would begin in early May, after lawmakers return from a two-week Easter break. With polls showing rising public anxiety about the tide of red ink, many lawmakers say they cannot vote to raise the debt limit without some new mechanism to control spending.

Obama never mentioned the highly technical issue of the debt limit, casting the congressional discussions as an effort to “find common ground” in “this larger debate we’re having about the size and role of government.” But lawmakers and other observers said they had little doubt about the true aim of the talks, which the president said should include 16 lawmakers — four from each party in each chamber.

“This is the ‘debt crisis avoidance committee,’ ” said Robert L. Bixby, executive director of the nonprofit Concord Coalition, which advocates for balanced budgets. “Since there’s not a whole lot of time to actually fix Medicare and Social Security and rewrite the tax code, they are probably going to resort to some sort of procedural device,” he said.

The White House has urged Congress to approve an increase in the debt limit without attaching other provisions, an idea lawmakers in both parties call unrealistic. But after meeting with the president early Wednesday, House Speaker John A. Boehner (R-Ohio) said Obama signaled that he might be willing to consider a bill that includes spending limits.

In fact, the president offered his own alternative Wednesday: a “debt fail-safe trigger” that would cut spending across the board if lawmakers did not approve policies that would set the debt on a downward path by 2014. The trigger should spare Social Security, Medicare and programs for the poor, Obama said, and should raise taxes by cutting dozens of tax breaks that benefit people and corporations.

“The American people are well past the point of believing that Washington will be able to make good on all its promises and that entitlement programs will be strong and solvent if Democrats are allowed to raise taxes,” Mc­Con­nell said in a statement.

Boehner also declared tax increases “a non-starter.” And, in an interview, House Budget Chair­man Paul Ryan (R-Wis.) accused Obama of abdicating leadership at a crucial point in the debate over the nation’s fiscal future with his proposal for another round of bipartisan talks.

“Delegating leadership to other people in other bodies is not what we need right now,” he said. “I think the president’s giving a speech today because he’s getting a lot of criticism for avoiding this issue. But you can’t fix these things by giving speeches.”

Reaction among Democrats was supportive but muted. Although Obama offered little guidance for navigating the immediate legislative battles, Democrats said he effectively highlighted the philosophical divide between the parties heading into the 2012 presidential campaign.

“He laid out the choices very clearly,” said Rep. Chris Van Hollen (Md.), the ranking Democrat on the Budget Committee. “The question is not whether you reduce the deficit, but how. And he clearly outlined the choices in front of the American people.”

Although Obama stumbled when describing some of his own proposals, he was eloquent in savaging the budget blueprint House Republicans announced last week, calling it a “deeply pessimistic” vision of the national character and of government’s ability to solve society’s most basic problems. He said the plan “would lead to a fundamentally different America than the one we’ve known throughout most of our history.”

The framework Obama offered builds on the budget proposal he sent to Congress in February and adds recommendations from the bipartisan fiscal commission he appointed last year.

That panel proposed to cut $4 trillion from deficits over a decade. The House GOP plan would cut deficits by about $4.4 trillion over a decade. Obama proposed to reduce borrowing by $4 trillion over 12 years, including $3 trillion over the next 10 years.

In addition to detailing his plan, the president tried to explain how the nation dug itself so deeply into hock. Among the culprits, he said, are politicians who tell people the debt is driven by “waste and abuse” rather than spending on valued programs, such as a strong military, education, Social Security and Medicare.

“Because all this spending is popular with both Republicans and Democrats alike, and because nobody wants to pay higher taxes, politicians are often eager to feed the impression that solving the problem is just a matter of eliminating waste and abuse,” he said.

But Obama has at times done the same. In his first address to Congress, one month after taking office, he pledged to cut deficits in half by the end of his first term. And he said he would start by going “line by line through the federal budget in order to eliminate wasteful and ineffective programs.” His team, he said, had already identified $2 trillion in savings over the next decade.

The assertion was false. Although Obama’s team had forecast a $2 trillion reduction in the deficit, it was not through cutting wasteful programs. Half of it would come through lower projected spending on the wars in Iraq and Afghanistan. Most of the rest would come from higher taxes.

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